Multi-component System by Karthiga Nagarajan

Composition of a mixture

karthigan1 — 2020-10-02 03:12:04 UTC

Mole number (or) Mass
Mole fraction (or) Mass fraction

Governing Equation

karthigan1 — 2020-10-02 03:13:44 UTC

a) Thermodynamic property of mixture given as function of P, T and composition
b) Gibbs Energy is Generating Function

Independent Variable

karthigan1 — 2020-10-02 03:16:06 UTC

Mixture with N species
a) Mole number (or) mass of species: All the parameters are independent of each other
b) Mole fraction (or) Mass fraction: (N-1) parameters are independent of each other

Definition

karthigan1 — 2020-10-02 03:18:44 UTC

Change in property while mixing streams (of different composition/T/P) to form a mixture

Significance

karthigan1 — 2020-10-02 03:19:40 UTC

Mixing Process
a) Expansion (or) Contraction - Volume change
b) Exothermic, endothermic. athermal - Enthalpy change
c) Spontaneous (or) Non-spontaneous - Entropy (or) Gibb free energy change

Definition

karthigan1 — 2020-10-02 03:37:20 UTC

Contribution of a species toward total mixture property

Features

karthigan1 — 2020-10-02 03:37:45 UTC

a) Depends on composition of species in a mixture
b) Obeys or follows linear property relations

Summability Relation

karthigan1 — 2020-10-02 03:39:11 UTC

Sum of partial property of all species will give mixture property

Gibbs-Duhem Equation

karthigan1 — 2020-10-02 03:39:50 UTC

Partial molar property of species in mixture are dependent on each other.
Partial molar property varies with changes in P, T and composition during a process satisfying G-D equation

Mixture dominant in one species

karthigan1 — 2020-10-02 03:41:09 UTC

Partial property/mixture property will be pure species property of the dominant species

Diluted species do have partial molar property and designated as partial property at infinite dilution limit

Definition

karthigan1 — 2020-10-02 03:43:31 UTC

No interaction among the molecules
Molecules occupy small volume compared to the mixture volume

Thermodynamic property

karthigan1 — 2020-10-02 03:44:33 UTC

IG mixture: Function of pure species ideal gas property (at mixture T & P) and composition

Fugacity of species: Partial Pressure of species

Fugacity coefficient of species: One

Multi-Phase Equilibrium Criteria

karthigan1 — 2020-10-02 03:46:13 UTC

Equality of Chemical Potential of Species in each phase at constant T and P

Multi-component system

karthigan1 — 2020-10-02 03:47:04 UTC

Different Chemical species in the mixture

Interaction among molecules of same chemical species - Like-Like

Interaction among molecules of different chemical species - Unlike

Properties of Mixing

karthigan1 — 2020-10-02 03:48:40 UTC

Mixing pure ideal gases to form an ideal gas mixture at Constant T and P

Volume of mixing: Zero
Heat effects of mixing: Athermal
Spontaneity of mixing: Spontaneous (Entropy change will always be positive & Gibbs Free energy change will always be negative)

Definition

karthigan1 — 2020-10-02 03:50:01 UTC

Molecules are of similar chemical nature
Interaction among similar and dissimilar molecules will be of same magnitude

Thermodynamic property

karthigan1 — 2020-10-02 03:55:53 UTC

Ideal Solution: Function of pure species property (at mixture T & P) and composition

Fugacity of species: Lewis-Randall (Pure species fugacity x composition)

Fugacity coefficient of species: Pure species fugacity coefficient

Properties of Mixing

karthigan1 — 2020-10-02 03:57:32 UTC

Mixing similar pure chemical species to form an ideal solution at Constant T and P

Volume of mixing: Zero
Heat Effects of mixing: Athermal
Spontaneity of mixing: Spontaneous (Entropy change will always be positive & Gibbs Free energy change will always be negative)

Are the derivations important?

karthigan1 — 2021-09-30 05:44:05 UTC

Yes. Understanding the derivation will help you to identify the constraints/assumptions/ limitations of the equation.

You will be able to judge whether an equation can be applied to a system in problem solving based on the limitations/constraints/ assumptions used to derive the equation.

For instance,
Property relations derived for ideal gas mixture model are in terms of pure species ideal gas property.
While performing property of mixing calculation for an ideal gas mixture, it is essential to write the pure species property equations based on mixture conditions only (P, T). This is applicable for the equations derived for ideal solution model as well.

Property relations for ideal gas mixture and ideal solution are molar properties and hence composition parameter in the equations are in terms of mole fractions (y_i or x_i).
While performing property of mixing calculation it is essential to evaluate the total property of the initial and final streams.

Permissible Assumptions (Unless otherwise stated)

karthigan1 — 2021-10-05 02:21:30 UTC

Gaseous mixture at Low P (<< 10 bar): Ideal Gas Mixture
Mixture of chemically similar species: Ideal Solution

karthigan1 — 2022-10-05 15:03:48 UTC

It was mentioned that the composition of a species in a mixture will be considered dependent if it is expressed in mole fractions. Suppose some of the species in the mixture can react, then the product of the reaction will also be a part of the composition of the mixture right? In that case, the amount of product will depend on the amount of the reactants. So can we consider that presence of a reaction will make the composition dependent too?

In the lecture we talk about the number of independent variables required to describe a system in a mathematical equation. If there are N chemical species in a system, there will be N independent variables if composition is expressed as mole numbers. There will be N-1 independent variables if composition is expressed in terms of mole fraction.

Mathematical expression will be a description of how composition changes in a reacting or non-reacting system.

Can you please show how the partial molar properties for a binary mixture was derived from the summability relations and the Gibbs-Duhem equation?

2023-10-12 06:26:31 UTC

Partial Molar property for a binary mixture

karthigan1 — 2023-10-12 06:30:55 UTC

Can we end early today?

2023-10-12 06:53:56 UTC

For Problem 1 part (b)

2023-10-12 07:41:24 UTC

You mentioned del(nH) / del(n_i) is valid as n_i can be changed while the other mole numbers of other species remain constant. How is this possible as all the mole numbers add up to n? If n_i changes, will the other mole numbers not change such that the total number of moles remains to be n?

Hi Prof, Where are we able to find the annotated slides for week 7 and week 8?

2023-10-12 08:09:45 UTC

I have a class at 5 and need to leave at 430

2023-10-12 08:30:24 UTC

Ive been lost since year 1 what do i do now 💀

2023-10-12 08:50:24 UTC

Remove quiz mark component

2023-10-12 10:00:52 UTC

Lecture quizzes would be best to act as an attendance check and ungraded to best allow us to firm our understanding rather than being demoralising.

For a pure component, chemical potential is total Gibbs free energy

2023-10-12 12:30:11 UTC

Hello, I don't understand why this statement is false, as I expect the Gibbs free energy to be due purely to the component

Ideal Gas Mixture Enthalpy

2023-10-15 02:44:20 UTC

For any ideal gas mixture that is formed isothermally, is the enthalpy change of mixing always going to be 0, since enthalpy change for ideal gas is only dependent on temperature?

Ideal Solution moles

2023-10-15 14:49:02 UTC

Why is there the assumption that the number of moles of heptane and decane at the beginning (n1 and n2) is equal to the final number of moles of heptane and decane?

Q4b

2023-10-17 13:15:56 UTC

Hi prof in the lecture, you mentioned that the R term can be cancelled off as there is no composition dependent term. But if we still factor it in, will it make much of a difference to the final answer?

2023-10-17 17:41:32 UTC

Just checking my understanding.

We assumed the solution behaves like an ideal gas mixture at the denominator. Therefore, partial pressure = xi * P, like a gas where pi = yi * P. As i understand there is different computation methods for partial pressure of liquid solutions i.e. Henry's Law, therefore this equation is only applicable only in this special case because we are treating the solution like an ideal gas?

Enthalpy and pressure

2023-10-18 02:38:27 UTC

Why is the enthalpy of an ideal gas independent of pressure?

So many theoretical derivations

2023-10-19 07:48:58 UTC

Prof, at this point, my grades also theoretical

2023-10-21 13:58:32 UTC

Based on the final S equation it has '-Rsum(yi * lnyi)' at the back. May I know why the pure species at the initial state do not have their respective R*yi*Lnyi at their back?

From week 8 practice question 1

2023-10-28 06:21:46 UTC

I'm getting answers that are off by 2-3 g. Is this acceptable? Thanks, prof!

From week 8 practice question 2

2023-10-28 08:27:38 UTC

I am unable to derive the solution enthalpy as in part a (which also needs to be used in part d). The provided answer is 100x₁ + 80x₂ + 8x₁x₂, which is different from H_final as seen in my working above. Please advise, prof. Thank you!

From Week 8 lecture quiz

2023-10-29 11:34:12 UTC

Raoult's law dictates that the partial vapour pressure exerted by a component is equal to its absolute vapour pressure times its molar fraction in a mixture.

By that logic, the partial pressures of both components are 1.5 bar as they are equimolar. As both components are ideal gases, we know that partial molar volume, Vig = V = RT/P.

The answer for the quiz question is that the fugacity of propane in the mixture is 1.5 bar as it is an ideal gas and thus, its fugacity in the mixture is equal to its vapour pressure.

If P is equal to 1.5 bar, why is the first option in the image incorrect?

Why is P equal to the system pressure when calculating the partial molar volume, but P is equal to the partial pressure when calculating the fugacity?

From week 8 practice question 5

2023-10-29 13:04:23 UTC

The question requires total entropy generation (J/K), not molar entropy generation (J/K-mol). How can I calculate it when the number of moles of compartment A, n_A, is not provided?

2023-11-04 09:12:49 UTC

hi prof why is it that delta Vmix = H^E?

should it not be delta Vmix = V^E?

Psat at 373 K = 500 Pa. As P - Psat = 500 - 300 = 200 kPa < 10 bar, is it valid to make the assumption that the fugacity coefficient is 1?

2023-11-05 11:26:04 UTC

1) Or is this condition only valid to assume that the Poynting correction factor is 1?

2) Can we only make the assumption that the fugacity coefficient equals 1 when Psat is very small, not when P - Psat << 10 bar?

Heat of mixing

2023-11-19 06:57:11 UTC

Hi prof, would the heat of mixing be still ΔH or ΔU if the mixing of two pure species is done under a close system (rigid container, meaning a non-constant P mixing process)?

2023-11-23 05:23:59 UTC

Hi prof, just to check, if the question states that adiabatic mixing is conducted, we can let ΔH_mix=0 right?

practice problem week 12, q3 - chem reaction equilibrium

2024-11-22 05:08:18 UTC

Hi Prof, I don't really understand how we can calculate the K, equilibrium constant for reactions. How did we calculate the value for delta(G_r) to be 17650 J/mol? Is there an equation?

2025-10-17 08:20:42 UTC

where can i find the concept map for this week's tut?

karthigan1 — 2025-10-23 06:22:18 UTC